Infinitely powerful entities

[Astner]

If you're writing for advanced mathematicians it might work.

Mathematics aside, it's still an interesting concept philosophically speaking.

Infinite means beyond measure; if you can't quantify one thing then you can't say another thing has more.

Infinity is mathematically defined as a concept greater than any finite values, and as shown, it is possible to quantify them.

It is not clear which letters represent sets, and which natural numbers.

Numbers are initially defined as sets,

0 ≡ Ø
1 ≡ S(0) = {Ø}
2 ≡ S(1) = {Ø, {Ø}}
3 ≡ S(2) ={Ø, {Ø}, {Ø, {Ø}}}
...
n+1 ≡ S = n ∪ {n},

so both.

If one entity can be mapped to the infinite set of integers (or it's power can, and the entity can be mapped to its power) then any other entity which can be mapped onto the same set has identically equal powers and is indistinguishable.

For power measured with cardinal numbers, yes, but not for power measured with ordinals.

My initial reaction, along with trying to muddle my way through your thesis is: what is your objective here?

To create an interesting and unique cosmology to expand my setting.

My initial reaction, along with trying to muddle my way through your thesis is: what is your objective here?

I would suggest that if you are intending a story most readers would, in the politest possible way, not be interested in having to keep referring to your 133 page paper on Omnipotence: The Cosmology, especially as it's fairly heavy math. Also the Abstract doesn't indicate a clear cut question for the paper, instead you have, as you have indicated got it as what appears to be a living document about enhancing understanding.

The idea is that the reader can either choose to accept the premise of various levels of infinity or he can read up on the logic behind it. This article is tailored to my work, and also shows the reader that I have an well-founded understanding of what I'm talking about.

This implies to me that there is either competition or heirachy between your entities? If competition then surely by some kind of 'godly' darwinism then there would only be one entity of infinite power as they would likely simply eliminate the competiton? If Heirachical then surely you would have your top dog, then infinite - 1 would be the next down, followed by infinite - 2 the next and so on and so forth.

The issue with it is that first and foremost these entities aren't subject to space-time and thus the process of eliminating becomes void, an entity that chooses to enter a universe with time limits himself.

Secondly, an entity A with a power of aleph-1 wouldn't have a problem with an entity B of power aleph-0. Because to A, B is just as insignificant as the universes and the mortals that inhabit them is to B.

Thirdly, there's not a finite amount of them, like the Greek pantheon you previously referred to.

And lastly, there's always a more powerful entity.

The question is how these characters use, or don't use their powers. If you have a collective of entities with such powers, do they have rules on how they may be used? My stories on the subject tend to deal with characters who bend or break such rules and the ensuing consequences; either for them or those they use the powers on.

Just like the Lovecraftian gods, they're mostly in the background.

And this is just scratching the surface of the cosmology. It later branches out into the illogical, and what I've titled the super-illogical, and so on. But I'm interested to hear what people think of this initial approach.

 

[Tyburn]

And lastly, there's always a more powerful entity.

Known in the Role-Playing Gamer universe as 'Summon Bigger Fish'.

So what you're saying is mathematically speaking infinity is a number so big you can't count to it or even imagine it's sheer enormity?

I'd always thought of the concept of infinity as something without beginning or end, a concept the human brain cannot really fully grasp. As mortal beings, we have a beginning, we have an end. There was something there before we began, there will be something there after we have ended. I'm not sure if I'm strolling into philosophical territory here, but the thing that's always bugged me is 'what was there before the Big Bang?', and if it was 'the Big Crunch' from the previous universe, how many universes have we been through to get to this point in time? What happened in the first ever universe, and what was there before that? For that matter, is this the first ever universe?

I think I'm starting to give myself a headache now, so I'm off to bed.

 

[Astner]

Known in the Role-Playing Gamer universe as 'Summon Bigger Fish'.

There's more to it than that. In a sensible axiomatic you will always be able to create something greater. But more importantly, as soon as you define an end to the food chain, you can define something beyond it.

So what you're saying is mathematically speaking infinity is a number so big you can't count to it or even imagine it's sheer enormity?

Infinity isn't a number, just like finiteness isn't a number.

But yes, even the smallest transfinite number is larger than every finite number.

 

[ralphkern]

Just so Im with you so far:

1. You are looking at a universe, or mulitverse in which a series of infinitly powerful beings exist. Infinite is quantifiable in that some are more powerfiul than others, to the point where a subordinate infinitly powerful entity is as irrelevant as an ant to the superior.

2. None of these entities are subject to space or time.

3. Your comment of 'defining the end of the food chain' meaning you can define something beyond it suggests that there is potnetially an infinite about of these entities.

Lets look at this thread another way. what would be the thrust of your story? can we have a brief back cover blurb style summary. I think it wouldd be a very interesting, but difficult narrative to pull off but im struggling to see how it would actually translate into a story, which i presume is the end result of what your looking at?

 

[Astner]

You are looking at a universe, or mulitverse in which a series of infinitly powerful beings exist. Infinite is quantifiable in that some are more powerfiul than others, to the point where a subordinate infinitly powerful entity is as irrelevant as an ant to the superior.

These entities would exist outside the universe, multi₁verse, multi₂verse, ..., omni₁verse, omni₂verse, etc.

None of these entities are subject to space or time.

Right.

Your comment of 'defining the end of the food chain' meaning you can define something beyond it suggests that there is potnetially an infinite amount of these entities.

Yes, they're infinitely many of them. But also infinitely many of them of equal power.

For instance, the smallest infinite ordinal, ω, would be the power-level of infinitely many entities.

Lets look at this thread another way. what would be the thrust of your story? can we have a brief back cover blurb style summary. I think it wouldd be a very interesting, but difficult narrative to pull off but im struggling to see how it would actually translate into a story, which i presume is the end result of what your looking at?

The cosmology is actually a separate work from the main story. However, the story will make some brief overlaps with the cosmology.

 

[Sapheron]

Do the characters within your world understand these things? Do the point of view characters? If they don't, an explanation that gets the general idea, but at the same time makes no sense and doesn't explain it (for example, and this isn't said negatively, your first post in the thread) is entirely sufficient.

I have hit similar problems when discussing immortal beings in some of my stories who are utterly incapable of death. Their attempts to explain a lot of what they are to others don't come across well, because who could possibly have a clue what they're on about?

In the same way, if your infinitely powerful eldritch being thingies are what they are, how is any character going to fully understand? And if the characters through which the story is being shown don't understand, then there's no real need for the reader to understand either.

Having read some more posts it would appear that you don't actually plan to have this in the story, but in a sort of 'background section' or somesuch. Best of luck if you want to put that together but I doubt that many readers would be interested in reading it if its as complex and mathematicsish as it looks like it would end up form this thread.

 

[ralphkern]

And the blurb ?

 

[Beef]

My brain is melting reading this stuff. How can something have infinite power? How does this power manifest itself, I mean, practically? A being that can do anything? How would such a being demonstrate the truth of this claim?

I know diddly-squat about maths. I wish that weren't the case, but it is. Maybe when you're explaining this sort of thing in the story, you can have an idiot character there to scratch his head and make confused noises while this is all being explained. Just to put people like me at ease